The question is basically asking<em> "What is 1¼ × 6?"</em> There are multiple ways to arrive at a solution for this. The first is to break the 1¼ into parts. 1¼ = 1 + ¼. When we multiply 1¼ by 6, that's equal to 1×6 + ¼×6. 1×6 = 6. ¼×6 = 6/4 = 1½. 6 + 1½ = 7½ hours
You could also put 1¼ as an improper fraction and then multiply. 1¼ = 1 + ¼. 1 = 4/4. 4/4 + 1/4 = 5/4. 5/4 × 6 = (5×6)/4 = 30/4. 30/4 = 15/2 = 7½ hours